NBER WORKING PAPER SERIES
WHAT DETERMINES EXPECTED INTERNATIONAL ASSET RETURNS?
Campbell R. Harvey Bruno Solnik
GuofuThou
WorkingPaper No. 4660
NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue
Cambridge, MA 02138 February 1994
Part of this paper waswrittenwhile the first author was visiting the Graduate School of Business at the University of Chicago. We are grateful for comments received from seminar participants at Cornell and Rochester as well as the comments of Wayne Ferson. Harvey's research is supported by the Batterymarch Fellowship. This paper is part of NBER's research program in Asset Pricing. Any opinions expressed are those of the authors and notthose of the National Bureau of Economic Research.
NBER WorkingPaper#4660
February 1994
WHAT DETERMINES EXPECTED INTERNATIONAL ASSET RETURNS?
ABSTRACT
This paper characterizes the forces that determine time-variation in expected international asset returns. We offer a number of innovations. By using the latent factor technique, we do
not have to prespecily the sources of risk. We solve for the Latent premiums and characterize their time-variation. We find evidence that the first factor premium resembles the expected
return on the world market portIolio. However, the inclusion of this premium alone is not
sufficient to explain the conditional variation in the returns. We find evidence of a second factor premium which is related to foreign exchange risk. Our sample includes new data on both international industry portfolios and international fixed income portfolios. We find that the two latent factor model performs better in explaining the conditional variation in asset returns than
a prespecified two factor model. Finally, we show that differences in the risk loadings are
important in accounting for the cross-sectional variation in the international returns.
Campbell R. Harvey Bruno Solnik
The Fuqua School of Business HEC School of Management
Duke University 78351 Jouy-en-Josas Cedex
Durham, NC 27706 FRANCE
and NEER Guofu Thou
Department of Economics Washington University One Brookings Drive St. Louis, MO 63130
1. Introduction
International asset pricing models of Solnik (1974, 1983), Stulz (1981) and Adler and Dumas (1983) provide a framework to determine why expected asset returns differ across countries. Differential expected returns, in these models, are linked to differences in exposures to global risk factors.
Given the null hypothesis of world market integration, asset pricing theories typically start with a representative world investor maximizing expected utility. First-order conditions imply an Euler equation which says that the conditionally expected product of the total asset return times the marginal rate of substitution is equal to a constant. Linearization of the Euler equation shows that expected returns are linearly related to risk. However, there are many possible choices in the specification of the risk factors.
In Stulz (1981), expected returns are linear in a measure of world consump-tion risk. However, even in countries with the most sophisticated data collecconsump-tion procedures, consumption data suffers from a number of disadvantages.1 As a result, it is problematic to estimate consumption risk of asset returns.
Solnik (1974) develops an international version of the Sharpe (1964) and Lintner (1965) capital asset pricing model where national investors differ in their consumption baskets and care about returns measured in their domestic currency. Adler and Dumas (1983) extend this model by allowing for stochastic national in-flation. This approach does not suffer from the disadvantages that follow the use of consumption data, but requires stronger assumptions on consumption tastes. In these models, the common risk factor is the return on a value-weighted world eq-uity market portfolio, hedged against currency risk. Unfortunately, the amount of currency hedging that enters this common factor depends on the individuals'
util-1 For a description of the problems with U.S. consumption data, see
Har-vey (1988), Breeden, Gibbons and Litzenberger (1989) and Ferson and HarHar-vey
(1992). International consumption data is used in Braun, Constantinides and
Ferson (1994). Wheatley (1988) uses the consumption framework to test the in-tegration international capital markets.
ity function and relative wealth, and is not directly observable. Given the absence of observable market weights for the currencies entering the common risk factor, this model is empirically equivalent to a multi-risk factor model with a world eq-uity market portfolio factor and currency risk factors. Under very restrictive (and unrealistic) assumptions about exchange rate uncertainty, this model reduces to a single observable risk factor model. For example, if purchasing power parity holds exactly at every instant, Grauer, Litzenberger and Stehle (1976) have shown that the world equity market portfolio would be the sole international risk factor. •
A third route involves the specification of multivariate linear proxy for marginal utility. This representation, follows the work of Merton (1973), Ross (1976) and Solnik (1983), and suggests that expected returns are determined by exposures to many sources of risk. One difficulty with this approach is the iden-tification of the set of factors.
While the asset pricing theories link average returns to average risk, they can also be used to study the time-variation in expected returns. Harvey (1991a), Sol-nik (1993), Campbell and Hamac (1992), Ferson and Harvey (1993) and Bansal, Hsieh and Viswanathan (1993) document that returns on many international eq-uity portfolios are predictable. The asset pricing theories are required to explain
both the changing cross-sectional differences in performance through time andthe
time-series predictability of the country equities.
Issues such as the integration of world capital markets and abnormal per-formance of any individual country cannot be answered without reference to an asset pricing theory. Indeed, there are a number of questions related to the as-set pricing specification. How many factors are necessary to describe the time-variation in expected returns? What are the sources of risk? Can we characterize the time-variation in the reward per unit of sensitivity to the risk? Answers to these questions may help identify the most useful paradigm for international asset pricing. Identification of the forces that shape expected returns have immediate implications for dynamic portfolio strategies.
This paper uses the latent factors method developed by Hansen and Hodrick (1983) and Gibbons and Ferson (1985) to characterize conditionally expected
in-ternational asset returns.2 We apply this method to 18 country index returns as well as new data on 18 international industry portfolio returns and 8 bond port-folio returns. We offer important innovations. An advantage of the latent factor technique is that the researcher is not required to take a stand on the composi-tion of the set of fundamental factors. In contrast to previous applicacomposi-tions, our idea is to solve for the expected risk premiums from the latent factor estimation, characterize their time-series variation and try to understand what predetermined factors account for their movements.
To recover the latent premiums and risk loadings, it is necessary to assume that the risk loadings are constant. However, this assumption may not be un-reasonable given that we study diversified portfolios of stocks rather than single issues. Our results indicate that the first risk premium resembles the expected return on a world market portfolio. However, this premium is not sufficient to characterize the variation in expected returns. A second premium, which is more complex to characterize, is also important. For our bond sample, this premium is related to foreign exchange returns. Our results indicate that expected returns are adequately characterized by two latent factors. Diagnostics and comparisons reveal that the latent factor model has distinct advantages over a prespecifled two factor model.
Finally, we examine the ability of the model to account for the cross-section as well as the time-series of expected asset returns. Using the two latent factor model and the 44 international portfolios, differences in risk loadings across portfolios has some ability to explain the cross-sectional variation in expected returns. These results suggest that the asset pricing framework provides a useful paradigm to explain differences in expected returns.
The paper is organized as follows. Section two provides the econometric methodology that we use to extract the expected factor premiums from the asset 2 This technique has been applied to U.S. and Japanese returns by Campbell and Hamao (1992), to 17 country returns by Harvey (1991a), G-7 equity and foreign exchange returns by Bekaert and Hodrick (1992) and daily G-7 returns by Chang, Pinnegar and Ravichandran (1991). Wheatley (1989) provides a critique of this method with reference to asset pricing tests.
returns. The data are described in the third section. The empirical results are presented in the fourth section. Some concluding remarks are offered in the final section.
2. Pricing models
2.1 Determinants of expected returns
Considera general K-factor asset pricing model of the form:
E(RjtIZt_j)
= .Ao(Z_1)+ thiAi(Zt_i) +
+
fliKAK(Zt_l), (1)i
= l,...,N,
t =
where=
the return on asset i between period t —1 and t,= the expected risk premium on the j-th latent factor,
=
themarket-wide information available at t, an L x 1 vector,•. , = the constant conditional betas of asset i,
N+1 =the number of assets (N>.K), and
T =
the number of periods.Notice that the above K-factor model allows the conditional risk premiums,
.X(Z_1)s, to vary over time as Z_1 varies. The conditional betas, however,
are assumed to be constant.
In terms of excess returns, the pricing relation (1) can be written:
=
b1A1(Z_1)+ ..
. + bKAK(Zt_l), (2)i
= 1,...,JV,t
=
where
=
Rfl — Ro is the return on the i-th asset in excess of the return onthe O-th asset (the O-th asset is arbitrarily ordered), and
=
f3
— flois the
'excess' conditional beta. To simplify the presentation, we write (2) in matrix
matrix of instrumental variables, A(Z) is a T x K matrix of risk premiums on the K factors and B is a K x N matrix of excess conditional betas. The matrix form of the K-factor pricing theory (2) is:
E(rIZ) =
A(Z)B. (3)To estimate the parameters, we assume the number of information variables is greater than the number of factors, i.e., L> K. Furthermore, we suppose through-out that .X(Z) and B have full column rank K. Otherwise, (3) will be reduced to a pricing model with the number of factors being less than K.
As in most studies, we assume that the expected returns are governed by the multivariate regression model:
=
OiZ_i,i
+ . . +OLZt_1,L +I =
1,...,
N, t =
1,...
,T,
(4)where en's are the disturbances which have zero means conditional on the instru-ments. Given the model (4), the pricing relationship (3) is valid if and only if the
multivariate regression coefficient matrix ehasrank K. In this case, we have:
H0:
e=AB,
(5)where A is a L x K matrix of risk premium multipliers. Therefore, a test of (5) is a test of the factor pricing theory. As shown in section 2.2, both A and B can be estimated from (4) under the restriction (5) and asset pricing tests can then be constructed.
Notice that the K factors (latent variables) are unknown as are the risk
premium multipliers. However, our goal is not just to report tests of the models restrictions. We also estimate the risk premium multipliers, A, and the excess conditional betas, B. Neither of the estimates is unique, since given estimates A
and B, any linear transformation of them, AC and C'B gives rise to the same
e
andso the same behavior of the excess asset returns1 where C is any K x Kinvertible matrix. However, the estimates of both A and B are determined up to a linear transformation. Furthermore, the estimation of eunderthe null is unique and the rank of 8 is uniquely determined.
To characterize the forces that determine the time-variation in the expected returns, we recover the risk premiums on the unknown factors, .A(Z). Following Zhou (1993), consistent moment estimators of A can be analytically obtained, and hence )(Z) can also be analytically estimated as follows. Given an estimate of A, A, we obtain from (3) and (4) an estimate of the risk premiums:
A(Z)=ZA.
(6)Because A is consistent, so is A(Z). Hence, we are able to estimate .X(Z) and characterize the variation in the risk premiums.
2.2. Estimation and tests
We apply the generalized method of moments (GMM) procedure for the esti-mation and latent factors tests. The idea of this method is to use sample moment conditions to replace those of the model. Intuitively, given these moment condi-tions, the sample moments should be close to zero at the true parameters. As the GMM estimator is the solution that minimizes the weighted sample moments, it should be close to the true parameters, Indeed, as shown by Hansen (1982), the 0MM estimator is consistent, i.e., converges to the true parameters with proba-bility one as sample size gets large. In our case, the model implies the following moment conditions:
E(h)=O,
htut®Zg_i,
(7)where ut is the N x 1 vector of model residuals from (3), Zg_1 is the L x 1 vector of the instruments, 0 is the Kronecker product and h an NL x 1 vector function of the residuals and instruments. Let g be the sample mean of ht:
NLx1.
(8)Hansen's (1982) 0MM estimator is the solution of:
where WT is a positive definite NL. x NL weighting matrix.
However, under the null that the rank of 8 is K, the unknown model parame-ters enter the quadratic form in a nonlinear way. it is not obvious, in general, how to analytically solve the 0MM optimization problem (9). Moreover, the numerical optimization of (9) is a nontrivial task. Fortunately, based on Zhou (1993), we can solve the estimator analytically for a class of patterned weighting matrices:
W,W1®W2, W1:NxN, W2:LxL.
The 0MM estimator of 8 is explicitly given by:o=Aa A:LxK, :KxN,
(10)where
A =
(Z'PZT2)"2E,
P ZW2Z', P : Tx T,
fl
= (Z'PZ'Z'PR,
ZzA,
r
: Tx
K,and E is the L x K matrix stacked by the 'standardized' eigenvectors (E'E =1K)
corresponding to the K largest eigenvalues of the L x L matrix:
(Z'PZ T2)"2(Z'PR T2)VV1(Z'PR T2)'(Z'PZ T2)'12.
(11)Furthermore, the minimum of Q isgiven by:
=
trWi(R'PR
T2) —— — 7K,
(12)where m• . ,7K are the K largest eigenvalues of the Lx L matrix given in (11). In practice, a consistent estimate of 8 is first analytically obtained as above by choosing the weighting matrix as the identity matrix. Then, a new weighting matrix can be computed:
WT [(fucu) ® @tzt__i)IT'.
(13)and a new 0MM estimator is obtained. Although both of the estimators are
consistent, the latter is expected to be superior because the new weighting matrix will better capture the underlying model residual distribution.
In latent variables models, as shown in Hansen (1982), a consistent estimator of the covariance matrix of the model residuals is given by:
Sr = LOitu ®
(14)Recall our discussion in section 2.1 that the parameter estimates of A and B are unique up to an non-singular linear transformation. To obtain unique estimates, we follow the usual normalization by assuming the first K x K matrix of B be the identity matrix, B = (1K, B2). This is equivalent to choosing the first K assets as the reference assets [see Gibbon and Ferson (1985)J. After this normalization,
thereareq=KL+K(N—K)=K(N—K+L)freeparameters.
Let D be an NE x q matrix of the first order derivatives of gj' with respect to the free parameters. Based on (13) and (14), we can construct a GMM test:
Hz a T(MTgT)'VT(MTgT), (15)
where V is a diagonal matrix, V' =
Diag(1/vi,...,1/v,o,...
,O), formed byv1 > ...
> v. > 0, the positive eigenvalues of the following NE x NL semi-definite matrix:a [I —
DT(D'TWTDT)'D'TWT]
5r [I —(16) where MT is an NE x NL matrix, of which the i-th row is the standardized eigen-vector corresponding to the i-th largest eigenvalue of fl for i =1,... , NE. As
shown in Zhou (1993), Hz is asymptotically x2 distributedwith degrees of
free-dom (L —
K)(N
—K).
This is the test of the model's overidentifying restrictions.The major advantage of using H1 instead of the conventional GMM test is that Hz is analytically available. In addition, the Hz test delivers the same inference as the conventional 0MM test, i.e., generating the same p-values.3
This is numerically verified by Zhou. (1993) in a smaller scale problem where the conventional 0MM test is easy to compute.
2.3 Characterizing the variation in the premiums and diagno3tics
With a set of prespecified variables, F, which are likely candidates for the underlying factors in the economy, we can construct prespecified risk premiums by linearly projecting them on the information variables, Z. We investigate whether this set of variables is correlated with A(Z), which are risk premiums on the latent factors. Since the estimation of A is only unique up to linear transformations, so are the estimated risk premiums .X(Z). We also report the canonical correlation of the estimated risk premiums and the collection of prespecified factor premiums.
The estimation of both the model with constant conditional risk and the model with time-varying risk implies a disturbance or a pricing error matrix:
u=r—A(Z)B.
(17)Disturbances will be affected by the number of factors that we allow in the esti-mation. The model implies that the conditional mean of the disturbance is zero.
One way to sllrnmarize the ability of the model to characterize the time variation in the expected returns is to study variance ratios. Let EM [rJ denote the model expected returns in (17). Following Ferson and Harvey (1991), we can compare the unconditional variance of these fitted returns to the unconditional variance of the fitted returns from the statistical projection model in (4) (denote as Ez(rJ):
VR1 = Var{EM[r]} (18)
Var{EzIrj}
If this ratio is close to one, then the expected returns from the model are closely mimicking the expected returns from the statistical model. As a result, the model 'explains' the time-variation in the expected returns.
We can also examine the variance of the part of the return that the model fails
to explain. Let EM (ii] denotethe fitted values of projecting the model residuals
in (17) on the instrumental variables. If the variance of these fitted values is large, then the model is doing a poor job of setting the conditional mean of the disturbances equal to zero. A second vaxiance ratio measures the ratio of the variance of these fitted values to the variance of the expected returns from the
statistical projection in (4):
19
-Var{Ez[r]}
If this ratio is close to zero, then the model pricing errors are not contributing to the predictable variation in the asset returns. These variance ratios are useful in
determiningnot just how many premiums we need but the relative contribution
of each additional premium.4
We also consider an additional diagnostic. The model implies that both the conditional and unconditional means of the disturbance matrix are zero. The tin-conditional mean is the average pricing error (APE). A large average pricing error indicates that the average return is much larger than the expected return implied by the model. Harvey's (1991a) implementation of the conditional CAPM resulted in large pricing errors for some international equity portfolios. We examine how these pricing errors are affected by increasing the number of risk factors.
Finally, we develop an analytical Wald test to examine whether or not there is structural change in the latent variables model. Suppose that the change occurs
after T1 periods. Let T2 be the rest of the periods, T1 + T2 = T. Intuitively, we
would like to compare the parameter estimates over the two subperiods. If there are substantially differences between the parameter estimates, we can reject the null that there is no structural change. Following Andrews and Fair (1988), a Wald test can be formed as follows:
WT =T(81—
82)'(Vi/lrir
+ V2/7r2r)'(Ôl —82), (20)
where Ôj and h2 are the analytical GMM estimators in the two subperiods, and
=
Ti/T
and lr2T =T2/T. LetV =
(D'TWTDTY'D'TWTSTWTDT(DIWTDT)',
(21)'
Fersonand Harvey (1993) provide a way to estimate the standard errors of thevariance ratios. However, to get the standard errors, they are only able to consider one asset at a time. Our formulation requires the simultaneous examination of many assets. Furthermore, the variance ratios are only meant to be diagnostic measures.
then V1 and V2, the estimators of the asymptotic covariances of h1and b2, are V valued at the two subperiods, respectively. In the Wald test, structural change is assessed by the stability of the parameters over two subperiods.
An alternative test may be developed that is based on the stability of the moments conditions over two subperiods. If there is no structural change, the sample moments in the second period should be close to zero even valued at the parameter estimator of the first period. This is the "predictive test" developed by Ghysels and Hall (1990). One advantage of the predictive test over the Wald test is that it uses only one estimator, making it useful in situations where it is difficult to obtain (3MM estimators. However, in our case we have analytical solutions, so
it is trivial for us to obtain 9 and 02.
Thepredictive test has a much complex form when the weighting matrix is not the optimal one, so we will use only the Wald test to test the structural change in the latent variables model.3. Data
3.1 Sources
The equity data in this study are drawn from Morgan Stanley Capital
Interna-tional (MSCI). Monthly data on equity indices for 16 OECD countries,5 Hong Kong and Singapore/Malaysia are available from December 1969 to September 1991. These indices are value weighted and are calculated with dividend reinvest-rnent. The equity indices are calculated from approximately 1500 stock returns which represents 83% of the total market value of the world's stock markets [see Schmidt (1990)]. Morgan Stanley also calculates a value-weighted world equity index which serves as the market portfolio. Returns are calculated in U.S. dollar terms.
The 16 OECD countries are Australia, Austria, Belgium, Canada, Denmark, France, Germany, Italy, Japan, the Netherlands, Norway, Spain, Sweden, Switzer-land, the United Kingdom, and the United States. Morgan Stanley also has data on Finland, Mexico and New Zealand but only from December 1987. These coun-tries are omitted.
The MSCI international indices are composed of stocks that broadly repre-sent stock compositionin the different countries. For example, Haney (1991a) reports a 99.1% correlation between the MSCI U.S. excess return and the New York Stock Exchange value-weighted return calculated by the Center for Research in Security Prices (CRSP) at the University of Chicago. There is a 95% corre-lation between the MSCI Japanese excess return and the Nilckei 225 return. An important difference between the MSCI indices and other national indices such as CRSP is the exclusion of investment companies and foreign domiciled companies. These stocks are excluded to avoid double counting.6
We introduce global industry indices which are also from Morgan Stanley Capital International.7 38 portfolios are available ranging from Aerospace and Military Technology to Wholesale and International Trade. As with the country portfolios, these indices are value weighted. In contrast to the country portfolios, the industry returns do not include dividends. However, later in the analysis we analyze an alternative set of industry portfolios that contain a dividend approxi-mation based on an identical U.S. industry grouping.
We form 18 international industry portfolios from these 38 industries. These industry portfolios, which are documented in figure 1, resemble the SIC groupings used in the industry portfolios in Breeden, Gibbons and Litzenberger (1989). The industry portfolios are formed by equally weighting the MSCI subindices in December 1969. This portfolio is held, without rebalancing, until the end of the
6 There
are disadvantages associated with the MSCI indices. First, the div-idends included in the monthly return are 12-month moving averages. Second, there are no adjustments for cross-corporate ownership [see MacDonald (1989),
Ftench and Poterba (1991) and Fedenia, Hodder and Triantis (1991)]
'
Industrial
structure and international stock returns is examined in Roll
(1992), Heston, Rouwenhorst, Wessels (1992) and Heston and Rouwenhorst (1993).
8
However, Breeden, Gibbons and Litzenberger (1989) use only 12 portfolios. We form 18 portfolios by breaking up the Basic Industries category into separate portfolios for Aerospace and Military Technology Chemicals, Forest Products, and Metals and Mining. We separate the Finance/REal Estate into two portfolios. Similarly, we separate Business Service industries from Personal Service industries. Finally, we add the Communications industry. In addition, we did not use the MSCI Multi-industry portfolio.
sample. Returns are calculated as the capital gain portion of this portfolio return. This produces a value-weighted return on an initially (December 1969) equally weighted investment.9
Our sample also includes bond returns from eight different countries: Canada, France, Germany, Japan, Netherlands, Switzerland, United Kingdom and United States. All of the bond indices, except for the U.S. index, are from Lombard Other & Cie (1992) and are reported on a daily basis in the Wall Street Journal Europe. These bond indices are based on a small sample of plain-vanilla, actively traded, long-term government bonds in each country [see Solnik (1993)J. The U.S. bond index is from Ibbotson Associates. All eight bonds are available from January
1971 through September 1991.
Since our study focusses on expected returns, it is important to correctly specify the information environment. The set of predetermined instrumental vari-ables follows Harvey (1991a) and includes: the world market return calculated in U.S. dollars (from Morgan Stanley Capital International), a dummy variable for the month of January, an exchange rate return index, the Standard and Poor's 500 dividend yield (from Standard and Poor's), the yield on a one-month Eurodol-lar deposit, the yield spread between Moody's Baa and Aaa rated bonds (from Moody's) and the excess return on a three month bill (from CRSP). The exchange rate return is based on the trade-weighted 10 countries' foreign exchange returns for the U.S. dollar investor. The exchange rate return.is determined by the change in the exchange rate plus a local 30-day Eurocurrency deposit. The variable is measured in excess of the 30-day Eurodollar rate. All of the instrumental variables are available through September 1991.
We use instrumental variables that are common to all assets for a number of reasons. We are interested in characterizing the common components of expected returns across all assets. In our framework, this variation is being driven solely by global risk premiums. In addition, the evidence that local information variables influence expected returns is weak. Harvey (1991a) finds that 2 of 17 countries The value weights in December 1969 where not available to us. This .is the reason that we initially equal weighted the portfolio. However, this is not very important since we can arbitrarily select portfolios for asset pricing tests.
are influenced by local infonnation. Ferson and Harvey (1993) find that 7 of the 18 countries are influenced by local information. However, the median increase in explanatory power for these countries is only 3.1 percent. As a result, we focus on a common set of instrumental variables.
3.2 Summary statistics
Table 1 reports the means, standard deviations and autocorrelations of the asset returns, and the instrumental variables. Returns are presented in U.S. dollar terms. The sample contains 247 monthly observations extending from March 1971 through September 1991.
The first panel of table 1 examines the country equity returns. The average country equity returns range from 10.4% per annum in Italy to 26.6% per annum for Hong Kong. However, the highest standard deviation is found for Hong Kong, 43.5% per annum. Significant first-order autocorrelation is detected for five coun-try returns: Austria, Denmark, Italy, Norway, and Singapore/Malaysia. These are fairly small portfolios compared to the capitalization of the world index'0 and may reflect infrequent trading of the stocks in these portfolios.
The next panel examines the global industry returns. These returns (as
provided by MSCI) only contain the capital appreciation part of the equity return. The average annualized returns range from 7.3% for the Utilities industry to 13.5% for the Aerospace and Military Technology grouping. There is a wide range of volatility from 15.1% for Utilities to 26.7% for Metals and Mining. On a relative basis, there is less autocorrelation in these index returns than the country indices. Only 3 of 18 industries exhibit first-order autocorrelation coefficients that are greater than two standard errors from zero. This could reflect the fact that these portfolios are diversified over many markets.
The next panel presents the eight bond returns in U.S. dollar terms. The annualized returns range from 8.8% (Canada) to 14.1% (Japan). However, these
'
Thelargest equity portfolio of this group, Italy, represents 1.4% of the MSCIreturns are greatly affected by the foreign exchange rate conversion. The volatility extends from 11.2% (Canada) to 17.6% (United Kingdom). No significant first-order autocorrelations are detected for the bond returns.
A number of the instrumental variables show a high degree of persistence. High autocorrelation is expected for the dividend yield variable because it is con-structed as a 12-term moving summation. The one-month Eurodollar rate and the Baa-Aaa yield spread also exhibit very high autocorrelation. The mean world market return over the sample is 12.8% with a standard deviation of 14.9%. In-terestingly, the average return exceeds the average U.S. equity return and the standard deviation is less than the U.S. return indicating that the U.S. equity portfolio is unconditionally dominated by the world portfolio over our sample.
Table 2 presents the results of linearly projecting the asset returns on the instrumental variables. The first panel considers the country index portfolios. The amount of variance explained for returns ranges from 2.1% for Italy to 12.2% for the United States. These results are consistcnt with those reported in Har-vey (1991a). The heteroskedasticity-consistent multivariate test of predictability provides convincing evidence against the null hypothesis of no predictability."
The amount of predictable variation in the industry portfolios is similar to the country index returns. Although, these industry portfolios are diversified across many different countries, each industry portfolio has a large U.S. component. Given that the instrumental variables are U.S. based, we expect to be able to predict these industry returns. Indeed, the statistical projection explains more than s% of the variance in more than half of the industry portfolios. The highest R2 is found for the Aerospace and Military Technology industry (14.2%) and the lowest is found for Textiles and ¶ftade (5.6%). The multivariate test suggests that the null hypothesis of constant expected returns can be rejected at the 0.01% level.
The next panel examines the predictability of the fixed income returns. The statistical projection is able to account for on average 5% of the variance of the S countries' bond returns. The highest R2 is found for the U.S. bond (7.9%) and
"
This test is based on the Pillai trace statistic. For a description, see Kirbythe lowest for the U.K. bond (3.1%). Although the predictability of the bond returns is less than the equity returns, the multivariate test shows that the null hypothesis of no predictable variation is rejected at the 3.4% level.
Figure 2 plots the fitted values from the three groups of the regressions. Overlaid on each plot are the fitted values from regressing the world market return on the same instrumental variables. It is clear from the figure that the expected asset returns, to some degree, move together. This is the case for both the equity and fixed income portfolios. One also learns from the figures that the variation in the expected returns is related to the variation in the expected world market return. Both of these findings are important. The common movement in the expected return suggests that a global asset pricing model has some chance at identifying the determinants of the expected international returns. The coherence with the expected world market return suggests that the first factor premium
may resemble the expected world market return —apremium implied by a world
version of the capital asset pricing model.
4. Results
4.1 The number of factors
Table 3 considers the number of factors necessary to characterize the predictable variation in the equity returns using the latent factor model with constant con-ditional risk loadings. The returns are measured in excess of the 30-day U.S. Treasury bill rate. Estimation is separately carried out for the two equity group-ings, country index returns and international industry returns.
For the country index returns, the results suggest a marginal rejection for the one to three factor models. The one factor results are consistent with the results of Harvey (1991a) who is unable to reject a conditional version of the Sharpe-Lintner model for 17 international equity portfolios.
For the industry returns, there is little evidence against the models' restric-tions. This contrast with the country grouping could be due to the industry data
oniy including the capital appreciation. As a result, we provide an alternative formulation of the industry portfolios which include a dividend approximation. The approximation is based on the dividend yields on U.S. stocks which fall into the same industry groupings detailed in figure 1.
The final part of table 3 examines the 8 fixed income portfolios. The test of the overidentifying conditions indicates that a one factor model is not rejected at conventional levels. However, the p-value jumps from 10.7% for the one factor model to 48.5% for the two factor model suggesting that more than one factor could be important.
4.2 Additional model diagnostics
While the statistical tests of the overidentifying restrictions were unable to
biguouslydistinguish between the one and two factor models, a different picture
emerges from the analysis of the pricing errors and variance ratios.
The first panel of table 4 presents average pricing errors and variance ratios for the country equity portfolios. Similar to the results in Harvey (1991a), the pricing errors of the one factor model are very large for some countries, particularly Hong Kong and Japan. The average pricing error, 0.431% per month, is about one third of the size of the average return. The average pricing error is reduced to only 0.181% with the two factor model.
A similar message is found in the variance ratios. With the one factor model, VR1 (explained by model) is 0.484 and VR2 (unexplained by model) is 0.589. This means that with the one factor model, the variance of the expected pricing errors is more than half of the predictable variance. However, with the two factor model, VR1 rises to 0.765 and VR2 falls to 0.303. With the three factor model, the VR1 and VR3 ratios are 0.845 and 0.226 respectively. This suggests that more than one factor is necessary to capture the country expected returns.
The second panel of table 4 carries out the same analysis for the 18 inter-national industry portfolios (without dividends). flrom table 3, we were lead to
believe that both the one and two factor models appear to fit these data better
than they do for the country index returns —inthat the p-values were higher. This
appears to be confirmed by low relative pricing errors. The average error with
the one factor model is 0.329%permonth which compares to an average return
of 0.885% per month. With the two factor model, the average error is reduced to 0.216% per month. However, the pricing error analysis is complicated by the lack of dividends in the data. One would expect lower or negative pricing error in returns which do not include dividends.
The variance ratio analysis indicates that the one factor model is describes 60% the time-variation in the expected returns. With the two factor model, the VR1 increases to 0.826. Not much is gained by going to the three factor model. The amount of variance explained increases by only 4%. The analysis on the industry returns with the dividend approximation reveals similar results. The one factor model explains 58% of the variation. When a second factor is introduced, the model explains 82% of the variation.
The final panel in table 4 examines how the model explains the variation in the international bond portfolios. The average pricing errors are small compared to the analysis of equities. The average bond returns from table 1 is .9% per month. The average pricing error reported in table 4 is 0.018% per month. The largest error is found for the Japanese bond. When a second factor is introduced, the pricing error is slightly reduced. The three factor model eliminates the average pricing error.
Similar to the equities, the first factor explains about 65% of the expected bond returns. When a second factor is introduced the proportion jumps to 83%. With three factors, 95% of the predictable variation is explained.
The pricing error and variance ratio analysis indicates that more than one factor is necessary to characterize the time-varying expected returns for all of the portfolios. This contrasts with the results reported in table 3 which suggested that one factor appeared to be enough (statistically) and provides motivation to explore other diagnostic measures.
[not reported]. A popular assumption in most conditional asset pricing tests is that the factor premiums are linear in the instrumental variables and the coefficients
are fixed through time.'2 Our tests suggest that the assumption of constant
coefficients is rejected.In our applications, we split the sample at the mid-point and let T1 =123,
=
124and T =
247. Coefficient stability is rejected for the one factor modelfor all the portfolios except the bond portfolio. For the two factor model, stability is rejected for the industry portfolios. The two factor bond model is marginally rejected. There is no evidence against stability for the country portfolios for the two factor model.
4.3 Characterizing the factor premiums
Given the assumptions of the econometric model, conditionally expected returns from the model are being driven by conditional variation in the risk premiums. There are two interesting questions that need to be addressed. First, do the model expected returns resemble the expected returns that result from the statistical projection of the asset returns on the instrumental variables. The variance ratios in table 4, indicate that the model fitted returns are indeed similar to the statistical fitted returns. Second, what are the model premiums? Do they have any economic interpretation?
The advantage of the technique of latent variables is that the researcher is not forced to take a stand on the specification of the proper set of factors. The model
is estimated and the minimum numberof premiums is extracted to characterize
the time variation in the expected returns. We now investigate the economic interpretation of the latent premiums from our estimation.
Most asset pricing theories suggest that there is a role for a 'world' market
portfolio as a factor. This is the international extension of the Sharpe (1964)and
Lintner (1965) capital asset pricing model. The conditional version of this model suggests that the market premium is the conditionally expected excess return on
a world market portfolio.
There is some theoretical guidance in choosing a second factor. International asset pricing models suggest that deviations from purchasing power parity could induce a premium associated with foreign exchange risk. For example in the model of Adler and Dumas (1983) and Dumas and Solnik (1993), covariances with different foreign exchange investments are priced. We summarize the exchange risk factor by the return on a trade weighted FX portfolio in 10 countries. In contrast to the FX portfolio used in Ferson and Harvey (1993), our portfolio is a return in that it include both the exchange rate change and the local Eurocurrency deposit rate. The factor is measured in excess of the 30-day 'fleasury bill rate.
Three other prespecified factors are identified. These factors are motivated by Chen, Roll and Ross (1986). They include the change in the price of oil, the change in OECD industrial production and the OECD inflation rate. In contrast to the first• two factors, these factors are not excess returns.
Table 5 presents the results of regressing these prespecifled factors on the information set. The results indicate the that 13.6% of the variation in the excess market return can be predicted with this set of instruments. The results in table 5 suggest that 8.5% of the change in the FX index is predictable. The projections indicate that the three macroecononñc factors are, to some degree, predictable. While only 3.3% of the variation in the oil price change can be accounted for
with the information set, over 27% ofthe variation in the OECD inflation rate is
predictable. Industrial production has an R2 of 1.41%.
In the lower panels of table 5, the coefficients associated with the instrumental variables representation of the latent premiums, A from (6), are reported for the two factor specification. The patterns and magnitudes of the coefficients on the factor 1 premium for the international equity returns resemble the coefficients on the prespecifled world excess returns regression. Specifically, the coefficients in the OLS regression on the four most significant variables Dlv, E$30, I3aa-Aaa and 3-1BILL are 9.8, -5.6, 15.2 and 5.2 and from the latent factor estimation are 15.8, -8.0, 19.9 and 5.6. Similar patterns are found for the international industry returns and the bond portfolio returns. It is more difficult to characterize the
second premium by examining the coefficients.
Table 6 shows the correlation between the expected values of these prespec-ifled premiums and the latent premiums. In the two factor estimation, the first factor premium has 95% correlation with the world market expected return when the country indices are examined and about 90% correlation when the interna-tional industries are used in the estimation. For the fixed income portfolios, the first factor has 83% correlation with the expected excess market return.
Although the factor premiums are not constrained to be identical across the asset groups, the correlation of the premiums is very high. The premium from the country estimation has 95% correlation with the premiums from the industry estimation. The country risk premium has 80% correlation with the first premium from the bond return estimation.
Figure 3 provides plots of the conditionally expected excess world market return and the first factor premium for the country index returns, the international industry returns (without dividends) and the bond samples. The graphs provide three interesting insights.
First, the expected factor premiums from all the asset sets are similar. This suggests that the same forces are determining expected returns in both the equity and bond markets. Second, the closeness of the factor premiums from the latent variable model and the conditionally expected excess return on the world market portfolio is striking. Third, there is a distinct business cycle pattern in the ex-pected values. While Fama and French (1989) and Ferson and Harvey (1991) have noted the business cycle patterns in U.S. expected returns, no one has documented any relation for international returns.
In figure 3, the NBER U.S. business cycle peaks and troughs are overlaid. Harvey (1991b) shows that there is an 88% correlation between the (3-7 business cycle and the U.S. business cycle over the 1969—1989 period. Interestingly, the highest premiums occur around business cycle troughs and the lowest premiums are found around business cycle peaks. This is found for all the business cycles in the sample. The intuition follows from investors demanding a high premium at the trough of the business cycle to give up consumption in order to invest in
equities. While these results are consistent with work on U.S. expected returns, the most recent business cycle provides some out-of-sample validation of these patterns.
Consistent with the analysis of the coefficients in table 5, the second factor premium is more difficult to characterize. For the bond sample, the second factor premium has a strong foreign exchange component (correlation 81%). However, the foreign exchange component is less important for the equity returns. For the country and industry returns, the second factor premium is related to the oil pre-mium and the inflation prepre-mium. In the bond returns sample, the second prepre-mium is related to. the inflation premium as well as the foreign exchange premium.
The fitted values of the second factor premium and the expected foreign exchange premium are presented in figure 4. Consistent with the correlation anal-ysis, there is little relation between the second latent factor and the prespecifled foreign exchange premium for the equity portfolio. However, the latent premium closely tracks the variation in the foreign exchange return for the bond returns.13
4.4 A comparison to a prespecifled two factor model
We compare the performance of the two latent factor model to a conditional asset pricing model with two prespecified factors. Given the analysis in tables 5 and 6, we choose the excess world market return and the change in the U.S. dollar FX index as the prespecifled factors.
Following Ferson (1990) and Harvey (1992), the following model is estimated:
(uj e) =
(f—Z6j
r—Z6j(u%ui)'u.r),
(22)where is a T x 2 matrix of the prespecified factors,
is1 is the factor innovation
matrix, r are the asset excess returns, and e are the pricing errors. The model
implies that E[( ft eg )
Zg_jj=
0. This model assumes that the factorpre-miums are linear in the information variables. In addition,
(u'f u,)'u?r is the
13 The
foreign exchange rate influence on the bond market premium is consistent with the resuits presented in During and Solnik (1993).
conditional beta which is assumed to be constant. This system is estimated with Hansen's (1982) GMM. With 2 factors, 8 instruments and N assets, there will be 8 x N overidentifying restrictions.
Table 7 presents the tests of the prespecified model as well as model diagnos-tics. For the country index portfolios, the model is not rejected at conventional
levels (p-value is 0.120). However,this model does not appear to perform as well
as the two factor latent variables model. Comparing the model diagnostics re-ported in tables 4 and 7, the average pricing error for the prespecified model is .240% per month for all the country returns compared to .181% for the latent factor model.
The prespecified model fails to explain many important portfolio expected returns such as Hong Kong which has an average error of 1.012% per month. More importantly, the VR2 ratio, which tells us the proportion of unexplained variance to the predictable variance, for the prespecified model is 52.6% for the country returns which is higher than the 30.3% reported in table 4.
A similar story emerges for the international industry portfolios (without div-idends). The average pricing error for the prespecified model is -0.576% compared with 0.216% for the latent factor model.
The average pricing error across the 18 portfolios using the prespecifled model is .123% compared to the .047% reported in table 4 for the latent factor model. The average pricing error for the Chemicals industry is -0.771% per month which is much different than the .080% per month with the latent factors model. Consistent with the country equity returns, the industry variance ratios are worse for the industry portfolios. The VR2 ratio is 36.7% compared to the 18.6% reported in table 4. However, the model's restrictions are not rejected at conventional levels with the prespecified factor model.
In the bond sample, the pricing errors are much higher with the prespecified factor model, 0.345% compared to 0.012% with the latent model. In addition, the variance ratio analysis indicates that little of the variation is explained by the two prespecified factors. In addition, there is evidence against the model's restrictions when the bond portfolios are examined. The p-value of the test of the
overidentifying restrictions is .032.
4.5 The relative importance of the factor premiums
Another method of diagnosing the importance of the factor premiums is to mea-sure the relative contribution of each premium to the conditionally expected re-turns. With the two factor model, the expected returns on asset i are determined by
=
bjAj
+ b2A2.The proportions of predictable variance accounted for by. the sources of risk are:
bVar(Ait)
b2Var(A2t)Prop1 =
Var(BA)
Prop2 = Var(BAg)where BA are the expected return generated by the asset pricing model, defined previously as EM [ri]. The variance ratios will not necessarily sum to unity because of a nonzero covariance between A and A2.
Variance decompositions are presented for both the latent factor and prespec-ified factor models in table 8. The risk loadings are also reported in this table. For the equity returns, the first source of risk is most important. The first risk premium accounts for 69% of the model expected returns for the country index returns. There is very high correlation between the factor premiums with the in-dustry portfolios. This is evident from the similarity of the A coefficients reported in table 5. As a result, only the one factor model is presented for the industry portfolios. In contrast to the equity portfolio, the first factor accounts for only 29% of the variation for the fixed income portfolios.
The second factor premium, while less overwhelming for the equities, plays an important role in the latent factor model. The second premium accounts for
28% ofthe variation in the model expected returns for the country indices and
70% ofthe variation of the bond portfolios.
similarities to the latent factor model.'4 For example, with the country returns
the first factor premium accounts for 80%ofthe expected return variation. The
second factor accounts for 17%. For the industry portfolios, the first premium accounts for 97% of the variation and the second premium only 3.3%. Finally, in the analysis of the fixed income portfolios, more than one factor is needed. The first factor premium explains only 28% of the variation while the second premium accounts for 85% of the variation.
Overall, the results suggest a role for a second factor when portfolios are grouped by countries or with fixed income portfolios. This contrasts with results presented in Ferson and Harvey (1991) who find that the market premium is overwhelmingly important in explaining the conditionally expected returns using U.S. data. Our results are supportive of the recent prespecified factor models proposed by Dumas and Solnik (1993) and Ferson and Harvey (1993). Both of these models include a role for exchange risk. Our results suggest that exchange risk is related to the second latent factor. However, it is also clear that the second factor is more complex.
4.6 The cross-sectional behavior of asset returns
Most of our analysis has concentrated on explaining the time-variation in the expected returns for 44 different portfolios. Our results indicate that the two latent factor model, with constant conditional risk, can account for about 75% of the conditionally expected returns across these 44 portfolios. In this formulation, the tine-variation is being driven by the latent premiums.
Asset pricing theories were originally developed to explain the cross-sectional behavior of expected returns. The model implies that assets with high risk should have high expected returns. Recently, Fama and French (1992) show "an absence of a relation between fiandaverage returns for 1963—1990" using various U.S.
'
Thevariance ratios of the latent factor and prespecified models cannot beequity portfolios and assuming that the a U.S. equity market portfolio is the sole factor. These findings challenge the usefulness of the present asset pricing models.
However, as emphasized in Roll (1977), Ross (1977) and Roll and Ross (1993), the mean-variance inefficiency of the benchmark could lead to the finding of no
significant relation between expected returns and $.Indeed,the results presented
in table 1, suggest that the U.S. market portfolio is unconditionally dominated by the world market portfolio.
While our data and approach are not directly comparable with Fama and
French (1992), some insight can be gained by exanhiningthelatent factor model's
ability to explain the cross-sectional behavior of the average asset returns. Figure 5 plots the risk loadings from the latent two factor model against theaverage excess returns over the 1971—1991 period. In contrast to the previous results, the loadings are based on a latent factor estimation which simultaneously considers all 44 assets. This estimation is only feasible using the analytical method with patterned weighting matrices detailed in section 2.2. From this cross-sectional scatter plot, it is evident that the some of highest expected returns are found with the portfolios with the highest risk loadings.
If a regression of average returns on the risk loadings is estimated, the R2 is 35% and the intercept is insignificantly different from zero. These results suggest that the asset pricing model provides a useful paradigm to explain both the cross-section and time-series behavior of expected asset returns.
5. Conclusions
This paper explores the sources of predictability in international bond and equity returns. While most research on international asset returns has relied upon either principal components analysis of the a post asset returns or a prespecified factor approach, we investigate the usefulness of a latent factors technique. The advantage of this approach is that the factors need not be specified.
factors necessary to characterize the expected returns. Our idea is to solve for the factor premiums and explore their time-series patterns as well as the correlation with a set of prespecified variables.
We test our model on using 18 country index returns as well as new data on 18 international industry portfolio returns and 8 fixed income portfolios. Although the statistical tests cannot reject a one-factor model, our diagnostics indicate that at least one additional factor is necessary to characterize the expected returns for the country index returns and the bond returns. With only two factor premiums,
77% of the predictable variation in 18 country index returns can be explained. Using the 18 international industry portfolios or the 8 bond portfolios, the two factor model accounts for 83% of the predictable variation.
Our characterization of the factor premiums suggest that the first premium has a strong resemblance to the expected excess returns on the world market portfolio. Consistent with the findings in the U.S. data of Fama. and F1ench (1989), we find that the world market risk premium is highest at business-cycle troughs and lowest and business-cycle peaks. We find that the counter-cyclical behavior of the first risk premium also obtains in the most recent business cycle
episode in 1990—1991.
The second premium is more difficult to characterize. For the bond returns, we find a high correlation between this premium and the conditionally expected change in a world foreign exchange returns index. This supports the role of foreign exchange risk proposed in Adler and Dumas (1983) and explored empirically in Ferson and Harvey (1993) and Dumas and Solnik (1993). However, the second latent factor appears to be characterized by more than a foreign exchange factor. We also compare the performance of the latent factor model to a prespecified conditional factor model. The prespecified model assumes the existence of two factors: the excess returns on the world equity portfolio and the foreign exchange returns index. The model diagnostics suggest that the latent factor model has distinct advantages over the prespecifled factor model in that the average pricing errors are smaller and the ability of the model to account for the expected returns is higher.
The relative importance of the risk premiums is also explored. Recent re-search, such as Ferson and Harvey (1991), suggests that the market factor is overwhelmingly important in explaining the time-series of expected asset returns. We find that the first factor premium is, indeed, the most important accounting
for about 80% of the model's predictable variation. However, the second factor
premium, is important for the country returns and very important for the bond returns.
Finally, we test the ability of the model to account for the cross-sectional behavior of expected returns. Recent work by Faina and &encli (1992) on U.S. equity data concludes that there is no significant relation between risk and return. Our results, which use international data and an international asset pricing frame-work, suggest that the cross-section of average returns is significantly related to the two risk loadings. The latent factor model appears to be a useful paradigm to help understand both the time-series and cross-sectional characteristics of ex-pected returns.
References
Adler, Michael and Bernard Dumas, 1983, International portfolio selection and corpo-ration finance: A synthesis, Journal of Finance 38, 925—984.
Andrews, Donald W. and Ray C. Fair, 1988, Inference in econometric models with structural change, Review of Economic Studies 55, 615-640.
Bansal, R.avi, David Hsieh and S. Viswanathan, 1993, A new approach to international
arbitrage pricing theory, .Journal of Finance 48, 1719—1747.
Bekaert, Geert and Robert Hodrick, 1992, Characterizing predictable components in excess returns on equity and foreign exchange markets, Journal of Finance 47,
467—509.
Braun, Philip, George Constantinides and Wayne E. Ferson, 1994, Time nonseparabil-ities and aggregate consumption: International evidence, International Economic
Review forthcoming.
Breeden, Douglas T., Michael R. Gibbons and Robert H. Litzenberger, 1989, Empirical tests of the consumption-oriented CAPM, Journal of Finance 44, 231-262. Campbell, John Y. and Yasushi Hamao, 1992, Predictable bond and stock returns in
the United States and Japan: A study of long-term capital market integration,
Journal of Finance 47, 43—70.
Chang, Eric C., J. Michael Pinegar and R. Ravichandran, 1991, Latent variables tests of the integration of European equity markets, Working paper, University of Mary-land.
Chen, Nai-fu, Richard Roll, and Stephen A. Ross, 1986, Economic forces and the stock
market, Journal of Business 59, 383—403.
Dumas, Bernard and Bruno Solnik, 1993, The world price of exchange rate risk, Working
paper, Group HEC.
Fazna, Eugene F. and Kenneth R. French, 1989, Business conditions and expected re-turns on stocks and bonds, Journal of Financial Economics 25, 23—50.
Fama, Eugene F. and Kenneth R. French, 1992, The cross-section of expected stock returns, Journal of Finance 47, 427—465.
Fedenia, Mark, James E. Hodder and Alexander J Triantis, 1991, Cross-holding and market return measures, Graduate School of Business, Stanford University. Ferson, Wayne E., 1990, Are the latent variables in time-varying expected returns
com-pensation for consumption risk, Journal of Finance 45, 397—430.
Ferson, Wayne E. and Campbell It Uarvey, 1991, The variation of economic risk
pre-miums, Journal of Political Economy 99, 285—315.
Ferson, Wayne E. and Campbell It. Haney, 1992, Seasonality and consumption-based
asset pricing, Journal of Finance 47, 511—552.
Ferson, Wayne E. and Campbell R. Harvey, 1993, The risk and predictability of inter-national equity returns, Review of Financial Studies 6, 527—566.
French, Kenneth R. and James Poterba, 1991, Were Japanese stock prices too high? Journal of Financial Economics 29, 337-364.
Ghysels, Eric and Alastair Hall, 1990, A test for structural stabifity of Euler conditions parameters estimated via the generalized method of moments estimator,
Iriterna-tional Economic Review 31, 355—364.
Gibbons, Michael R. and Wayne E. Ferson, 1985, Tests of asset pricing models with changing expectations and an unobservable market portfolio, Journal of Financial
Economics 14, 217—236.
Grauer, Fredrick L. A., Robert H. Litzenberger and Richard Stehle, 1976, Sharing rules and equilibrium in a international capital market under uncertainty, Journal of Financial Economics 3, 233-256.
Hansen, Lars P., 1982, Large sample properties of generalized method of moments
estimators, Econometrica 50, 1029—1054.
Hansen, Lan P. and Robert J. Hodrick, 1983, Risk averse speculation in forward foreign exchange markets: An econometric analysis of linear models, in Jacob A. Frenkel, ed.,: Exchange rates and international macroeconomics (University of Chicago Press, Chicago, IL).
Harvey, Campbell R., 1988, The real term structure and consumption growth, Journal of Financial Economics 22, 305-3M.
Harvey, Campbell It, 1991a, The world price of covariance risk, Journal of Finance 46,
111—157.
Harvey, Campbell it, 1991b, The term structure and world economic growth, Journal
of Fixed Income 1, 4—17.
Harvey, Campbell R., 1992, Conditional asset pricing with instrumental variables, Work-ing paper, Duke University.
Heston, Steven, and Geert Rouwenhorst, 1993, Does industrial structure explain the benefits of international diversification?, working paper, Yale School of Organiza-tion and Management.
Heston, Steven, Geert Rouwenhorst and Roberto E. Wessels, 1991, The structure of international stock returns, working paper, Yale School of Organization and Man-agement, October.
Kirby, Christopher M., 1993 A multivariate analysis of predictability in stock and bond returns, Working paper, Duke University, Durham, NC.
Lintner, John, 1965, The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets, Review of Economics and Statistics 47,
13—37.
Lombard, Odier & Cie, 1992, Introduction to the Bond Indices of Lombard, Odier El Cie, Geneva, Switzerland.
McDonald, Jack, 1989, The Mochiai Effect: Japanese Corporate Cross Holdings, Journal
of Portfolio Management, 90—94.
Merton, Robert C., 1973, An intertemporal capital asset pricing model, Econometrica
41, 867—887.
Roll, Richard, 1977, A critique of the asset pricing theory's tests, Journal of Financial
Economics 4, 129—176.
Roll, Richath, 1988, The international crash of October 1987, Financial Analysts
Jour-nal 44, 19—35.
Roll, Richard, 1992, Industrial structure and the comparative behavior of international stock market indexes, Journal of Finance 47, 3—42.
Roll, Richard and Stephen A. Ross, 1993, On the cross-sectional relation between ex-pected returns and betas, Journal of Finance forthcoming.
Ross, Stephen A., 1976, The arbitrage theory of capital asset pricing, Journal of
Eco-nomic Theory 13, 341—360.
Ross, Stephen A., 1977, The Capital Asset Pricing Model (CAPM), short sale restric-tions and related issues, Journal of Finance 32, 177—183.
Schmidt, Dana, 1990, Morgan Stanley Capital International (MSCI) indices, Morgan Stanley, New York, NY.
Sharpe, William, 1964, Capital asset prices: A theory of market equilibrium under
conditions of risk, Journal of Finance 19, 425—442.
Solnik, Bruno, 1974, An equilibrium model of the international capital market, Journal
of Economic Theory 8, 500—524.
Solnik, Bruno, 1983, International arbitrage pricing theory, Journal of Finance 38, 449—
457.
Solnik, Bruno, 1993, The performance of international asset allocation strategies using conditioning information, Journal of Empirical Finance 1, 33—55.
Stulz, René, 1981, A model of international asset pricing, Journal of Financial
Eco-nomics 9, 383-406.
Wheatley, Simon, 1988, Some tests of international equity integration, Journal of
Fi-nancial Economics 21, 177—212.
Wheatley, Simon, 1989, A critique of latent variable tests of asset pricing models,
Jour-nal of Financial Economics 23, 325—338.
Zhou, Guofu, 1993, Analytical 0MM tests: Asset pricing tests with time-varying risk premiums, Washington University, St. Louis.
Table I
Means, standard deviations and autocorrelations of international equity andbond returns calculated in U.S. doLlars and based on data Irom March 1971 to September 1991 (247 obs&vasions).
Variable
Autocontlasjon
Mean Mean SW. dew. p' m Pa P Pa Pg
(anti..) (gee.) lida return. Australia Autda Belgium Canada Deateark Paace Germany hongKong Italy Japan Netherlands Horny Siocapaa/Mshyda Spain Seden Switaerland United Kin$on. UniIgdStaS 24360 25907 16.333 21.320 17.734 15.968 14.773 26.593 10.400 21.118 26,987 16.319 20093 11.717 18.480 13863 17.545 11.500 10156 13.396 14.106 9.387 15.734 12.373 12.341 17.287 6.700 16.377 15.123 12.117 14123 9.009 15.942 11821 1.3.950 10181 27.745 23.495 20.973 19.736 19.757 25.653 21.797 43.466 27.140 23.037 16902 20936 52938 23.171 22.154 96.131 27.310 15.980 -0.014 0.167 0092 -0013 0016 0063 -0001 0053 0.143 0058 0.033 0.258 0.165 0224 0080 0048 0.101 0.022 -0053 0040 0.046 -0096 0.132 0.003 .0.017 4036 0.026 0012 4034 4.001 -0011 0004 -0028 -0063 0.093 -0.047 4008 0.033 0.036 0095 0.092 0.127 0.106 -0009 0093 0051 0.067 0.153 4032 0.043 0.053 0046 0.051 0015 0009 0.063 0.040 -0025 0.102 0.023 0062 4.035 0.074 0047 -0.100 4.075 0049 0080 4.014 0.006 0004 4_on -0042 0.025 0.039 -0056 -0.132 -0.045 0.054 4.000 0036 0067 0.056 0.031 0.045 4.023 0031 0001 4.007 0.052 0.041 0026 0034 0.043 0.079 0.000 0002 4.017 0.014 4.000 0.003 0.014 .0.002 0.121 0.003 4.026 0.059 4.027
International iedu.try return.(withoutdividends)
Acoapac. 4 Miit. 1thnolo
Capital Good. aemical. Coemw.ication. Ccnstnjdioo Consume DnnbIa Energy Finance
Food& Tobacco
Forert Product.
Leleere
Metal. and Mining
RealEstate Services—0u.iuias Services-Per.oo.J Textile 4 Thade Twportatica IJtllitie 13.522 10.563 6919 9.297 12.434 10.482 10.832 12.434 52.675 7.569 51.190 10024 14.4$? 9.929 11.190 13.540 10.466 7.257 10.760 3.763 7836 6.172 10.053 8.746 3.234 10.534 11.426 5.430 0.957 5.43? 20.609 0.375 9.702 11.944 6.655 6.130 23.320 18440 17.115 14.764 21833 18.400 23.585 19.702 15.545 20.646 20.002 26.703 27.781 17.432 17.134 23.301 16.900 15-063 0.105 0.050 0.035 0.101 0.005 0097 0021 0.174 0.115 0.036 0.177 0038 0.097 0.156 0.030 0.048 0-132 0.071 0.002 4.026 0.058 4.018 0.037 0.000 4.039 4.033 4.000 -0.068 0.058 4.075 0.004 -0.060 0.022 0040 0.016 4.075 4036 0.048 0.235 0023 4019 0.037 4014 0010 0.092 0.020 0.033 0.036 0.056 0.057 .0.037 4.013 4.017 4.021 4.017 4.054 4.026 4.133 0.056 0020 0.037 4.028 4.062 4.007 4.067 0.099 0.004 4.018 4.003 4.097 4-055 0,044 0028 0.017 0.037 4.003 0.064 0.022 0.063 0.134 0.072 -0.039 0.018 0.068 0.134 0.002 0.100 0052 0.083 0.015 0016 0020 0.035 0017 0.043 -0.006 4.009 4.024 0.012 0.039 4.102 0.062 0.025 0.044 0.006 4.037 4.014 - 0,015
Tabk I(continued)
.
-Vanable Mesa Mean
(aML.) (gin.) Sid. tv. -AIstocaneIatinn P p1 P12 p3 .
lnleniat.oosl bond l'd.Ini.
Canada Fhace Germany Japan Netherlands Switsedand United IGdom United Stats 8.824 11319 12.416 14.147 12.234 10.873 10.551 9.127 8.177 10.296 11.316 12.886 11.220 9.899 - 0.000 0.479 11.199 14.037 14.556 15.575 13.929 13.736 17296 11.254 0.021 0.035 0.042 0.090 0.097 0.093 0.059 0.067 0068 0.055 0.063 0.010 0.023 0.086 0.015 4.038 0.010 0.099 -0.040 0.054 -0.01! 0.015 4.189 4.139 -0.148 - 0.091 .0.005 0.048 0,013 0.080 0.003 4.004 0020 -0.003 0.056 0.085 .0.009 0033 4.007 .0010 4.012 o.o4 0.032 4.080 0.011 4.063 0.019 4.060 Inetminedal vseiabln Wdd return
GIG ct_nancy retisa
S&P 800 dividend yield
I month Eurodofla
Moody'. Baa-Ass yield
3 month-I month 'V. bill
- 22.768 1.617 4.163 t061 1.274 0.900 11.606 1.200 4.135 9.022 1.273 0.907 14.891 9.464 0.267 0.927 0.527 0.473 0.092 0.016 0.082 0.946 0.950 0.277 4.047 0.127 0.955 0.884 0.881 0018 0.045 0.066 0027 0.829 0.831 0002 4.010 0.050 0.000 0.772 0.795 -0008 0.060 . 0.033 0.663 0.558 0.437 0.086 0.015 0.004 0.472 0.138 0.079 0.031
Table 2
Thepredictability at international equity and bond returns calculated in US. dollars. Expected values are obtained by linearly
projecting on the iustrullIeotal variables. The instrumental variables are: aconstant,thelagged exc return on theMorgan
Stai.ley Capital International world equity Index, (WIth), the lagged return on the index ol investments in 10currencies,
(XRG10),the lagged dividend yield on the Standard and Poor's 500 stock index (Dlv),•dummy variable For the mouth ol
Januasy (JAN),thereturnona 30-day Eurodollardeposit(E$30), the yieldonMoody's Baaratedbonds less theyieldon
Moody'sMarated bonds (Baa-Aaa) and the return for holding a 90-day U.S. 'fteasury bill for one month lessthe return on
&30-day hill (90-30TH). Ileteroskedasticity-eoniiateat t-statistia are in brackets. Estimates are based onmonthly datafrom
1971:3—1991:09 (247 observations).
ronloljo
A-Country Index returns
tnteapt WRD..1 XRGIO,_j 3A14 D1V1_1 E630,_t Bn-M_1 00-3OTH1—i
R2/
Australia 0.004 0.266
f.:j
4098 0023 J3.378 4.502 (-2.359) -9.472 (-0.606) 11.56$ - 0,103 Austria 0.05' (2.720) 0.175 ('-"1 14.02114.004 -0026 (-1.706) 4.464 (-0.076) -1.616 I-'-°"l -25.133(-2.195) 3.416 (1.375) 0.052 0,024 Belgium 0.016 (0.8671 4.069 (4.695) 4061 (4.345) 0.014 (1.125) 11.42$ p.047) 4.651 1-3.6801 t061 (0.355) 4.333 t.55I) 0,064 0.037 Canada -0.006 1-0.3061 0.011 (0.986) -0.121 (-1082) 0010 [0.602) )I.244 4.829 (-2.215) —4.533 10384) p.08;r-2951 0.103 0.082 Deoa.s$ 0.033 (2.538) -0.215 (-233S) -0089 t-°-S°l 0.013 (1.305] -2.625 [4313) (-2.633)-3.972 9.701t'-'l
1.110 (0.639) 0.054 0.027 mace .0006 foil?) (0-08?)OSlO -0,131 (-0.635) 5.014 24.233 -7226 (-3-052) 4.610 (-0.333) 0.748(0)
0.054 5.027 Germany 0.005 (0.344) 003$ (0:293) .0.127 (0.650) -0.010 (-0.7571 12.709I-°l
-1.084 1-2.339) 0.753 (0.063) 2.288 (0.5171 0.038 0.007 Hong Kong 0.043 (0.864) 0.233 I'-°'l (-in.)4069 p434)0.064 3.209 10.2311 4.546 (-1037) 5.113 (0.398) 2.710 (0.432 0.050 0.022 Il-ely 4.014 (.0.643) 0.093 (0.837) 0.117 (0379) 0.022 (1.215) (1.419j11.67% .1.764 (-0.623) —7.306 (-0466) 0.819 (0.159) 0.02' -0.007 Japan 0.027 (1.235) 0.065 (0619) 0.083 (0.474) 0.003 10.25$) 1.632 10.350) 4,261 1-2.7181 P.46t11.7161 -2.115 (-0.516) 0.053 0026 Netlierlant -0.004 (4.3121 4.053 (.0.5781 4.044 (-0.331) 0.021 11.5101 13.835 (3.557) 4.326 1-3.6321 12.415 11.13$) 4.756 11.603] 0.092 0.065 Norway 0.035 (1233] 0.063 (0.383) 4.325 1-0602) 0.042 (1211] 2.339 (0.339) .1.413 (-0.523) -25.979 (-1.479) 5.774 (2.204) 0.035 0.007 Singepore/Malayala 0.023 (0.6591 0.066 (0.4251 .0.086 1-0.4311 0.075 (2.726) 8.104 (0.414) -5.383 (-1364) 2.715 (0.260) 12.3581JI.307 0.100 0.074 Spain 0